Subharmonic Oscillations in Nonlinear Systems

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Abstract
This paper deals with the subharmonic oscillations which occur in systems with nonlinear restoring force. It is first shown that the order of the subharmonics has a close connection to the form of the nonlinear characteristics. The subharmonic oscillation of order ⅓, i.e., the oscillation whose fundamental frequency is one‐third that of the applied force, is then particularly investigated for the cases in which the nonlinear characteristics are expressed by (1) cubic and (2) quintic functions. In both cases the stability problem of the periodic solution is discussed in detail according to the stability criterion given previously by the author. The analysis reveals that in the latter case (2) the second higher‐harmonic of the subharmonic, i.e., the oscillation of order ⅔ builds up with negative damping. This is verified by experiments in which the oscillation of order ⅔ causes the collapse of the original subharmonic oscillation.

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